{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropy\n",
    "Entropy measures the uncertainty associated with a probability distribution. If all values are more or less equally probable, the entropy is higher because we cannot predict the output of the system with certainty. On the other hand, if some items are much more probable than others, we can predict them with relative certainty. Such a system has low entropy. \n",
    "\n",
    "Let us see this for Gaussian distributions. The entropy of a Gaussian is directly related to its standard deviation $\\sigma$. The higher the $\\sigma$, the wider the Gaussian and thus higher the entropy. Gaussians with lower $\\sigma$ are more peaked and have lesser entropy. The entropy can be computed using the following formula.\n",
    "\n",
    "$$ H(X) = \\frac{1}{2} \\log(2 \\pi e \\sigma^2) $$\n",
    "\n",
    "We will now see this in PyTorch. Refer Section 6.2 of the book for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from torch.distributions import Normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy_gaussian_formula(sigma):\n",
    "    return 0.5 * torch.log(2 * math.pi * math.e * sigma * sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Normal(0, 10)\n",
    "\n",
    "# Compute entropy using the formula defined above\n",
    "H_formula = entropy_gaussian_formula(p.stddev)\n",
    "\n",
    "# Compute entropy using the PyTorch function call\n",
    "H = p.entropy()\n",
    "\n",
    "assert torch.isclose(H_formula, H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def entropy_plot(p, q, r):\n",
    "    x = np.linspace(-100, 100, 1000)\n",
    "    p_pdf = p.log_prob(torch.from_numpy(x)).exp()\n",
    "    q_pdf = q.log_prob(torch.from_numpy(x)).exp()\n",
    "    r_pdf = r.log_prob(torch.from_numpy(x)).exp()\n",
    "\n",
    "    p_entropy = p.entropy()\n",
    "    q_entropy = q.entropy()\n",
    "    r_entropy = r.entropy()\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 6))\n",
    "    ax.set_title(\"Gaussians with varying entropy\")\n",
    "    ax.set_ylabel(\"P(X)\")\n",
    "    ax.set_xlabel(\"X\")\n",
    "    ax.plot(x, p_pdf, 'green', label=\"p distribution. H = {:.2f}\".format(p_entropy))\n",
    "    ax.plot(x, q_pdf, 'blue', label=\"q distribution. H = {:.2f}\".format(q_entropy))\n",
    "    ax.plot(x, r_pdf, 'orange', label=\"r distribution. H = {:.2f}\".format(r_entropy))\n",
    "    ax.legend()\n",
    "\n",
    "# Instantiate two more Gaussians with higher variance\n",
    "q = Normal(0, 15)\n",
    "r = Normal(0, 25)\n",
    "\n",
    "entropy_plot(p, q, r)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
